Quasi-triangular and factorizable antisymmetric infinitesimal bialgebras

Manin Triples and Bialgebras of Left-Alia Algebras Associated with Invariant Theory

“…A bialgebra structure is a vector space equipped with both an algebra structure and a coalgebra structure satisfying certain compatible conditions. Some well-known examples of such structures include Lie bialgebras [14,15], which are closely related to Poisson-Lie groups and play an important role in the infinitesimalization of quantum groups, and antisymmetric infinitesimal bialgebras [16][17][18][19][20] as equivalent structures of double constructions of Frobenius algebras which are widely applied in the 2d topological field and string theory [21,22]. Recently, the notion of anti-pre-Lie bialgebras was studied in [23], which serves as a preliminary to supply a reasonable bialgebra theory for transposed Poisson algebras [24].…”